The data in the file radon.dat were collected from 1003 homes in Minnesota in
1987 (Tate, 1988) in order to estimate the prevalence and distribution of households with high indoor radon concentrations. The data are adapted from www.stat.berkeley.edu/users/statlabs/labs.html, the website for Nolan and Speed (2000). Since the investigators were interested in how radon levels varied across counties, each of the
87 counties in Minnesota served as a stratum. An SRS of telephone numbers from county telephone directories was selected in each county. When a household could not be contacted or was unwilling to participate in the study, an alternate telephone number was used, until the desired sample size in the stratum was reached.
b. Calculate the sampling weight for each observation, using the values for Nh and nh in the data file.
c. Treating the sample as a stratified random sample, estimate the average radon level for Minnesota homes, along with a 95% CI. Do the same for the response log (radon).
d. Estimate the total number of Minnesota homes that have radon level of 4 picocuries per liter (pCi/L) or higher, with a 95% CI. The U.S. Environmental Protection
Agency (2007) recommends fixing your home if the radon level is at least 4 pCi/L.